Write the Word or Phrase That Best Completes Each Statement $$M = 750 + 125 \sin \frac { \pi } { 6 } t$$

question 13

Essay

Write the word or phrase that best completes each statement or answers the question.
-Wildlife management personnel use predator-prey equations to model the populations of certain predators and
their prey in the wild. Suppose the population M of a predator after t months is given by $$M = 750 + 125 \sin \frac { \pi } { 6 } t$$ while the population N of its primary prey is given by $$N = 12,250 + 3050 \cos \frac { \pi } { 6 } t$$ Find the values of $t , 0 \leq t < 12$ , for which the predator population is 875 . Find the values of $t , 0 \leq t < 12$ , for which the prey population is 10,725 .

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Definitions:

Total Cost

The sum of all expenses incurred in the production of goods or services, including fixed and variable costs.

Total Revenue

The total income received by a firm from selling its goods or services before any costs or expenses are deducted.

Marginal Product

The rise in production resulting from the use of one more unit of input.

Value of the Marginal Product

The extra income produced from the use of an additional unit of input, like capital or labor.